Chaotic behavior of a class of discontinuous dynamical systems of fractional-order
Chaotic behavior of a class of discontinuous dynamical systems of fractional-order
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DOI：
10.1007/s11071-009-9612-y
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发表时间：
2010-06
影响因子：
5.6
通讯作者：
Marius-F. Danca
中科院分区：
文献类型：
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作者：
Marius-F. Danca
分析了一类分数阶不连续动力系统的混沌持久性。为此，首先利用Filippov正则化方法(Filippov in Differential Equipment in Difference Riguant Riguents，1988)将初值问题转化为分数阶集值问题，然后利用Cellina的近似选择定理(Aubin和Cellina在微分包含集值映射与生存理论中，1984；Aubin和Frankowska在集值分析中，1990)。将问题近似为单值分数阶问题，利用Diethelm等人提出的数值格式进行数值求解。(非线性动力。29：3-22,2002)对这类系统的两个典型例子进行了分析和仿真。
In this paper, the chaos persistence in a class of discontinuous dynamical systems of fractional-order is analyzed. To that end, the initial value problem is first transformed, by using the Filippov regularization (Filippov in Differential Equations with Discontinuous Right-Hand Sides, 1988), into a set-valued problem of fractional-order, then by Cellina’s approximate selection theorem (Aubin and Cellina in Differential Inclusions Set-valued Maps and Viability Theory, 1984; Aubin and Frankowska in Set-valued Analysis, 1990). The problem is approximated into a single-valued fractional-order problem, which is numerically solved by using a numerical scheme proposed by Diethelm et al. (Nonlinear Dyn. 29:3–22, 2002). Two typical examples of systems belonging to this class are analyzed and simulated.